The second property of note, provided by BCS theory, is the superconducting gap [\(\Delta (\omega ,T)\) ] equation that gives T\(_c\)  when linearized (\(\Delta \rightarrow 0)\)  and provides the frequency \(\omega \)  and temperature \(T\)  dependence of the energy gap that is responsible for many of the fascinating properties of superconductors: the fact that a perfect “super–conductor” can have a gap for excitations; this gap leads to a vanishing magnetic susceptibility in its interior; it is a basic player in zero resistivity; it severely alters thermodynamic, optical, and transport properties. The effect on the electronic specific heat, shown in Fig. REF , is to make it vanish exponentially as T\(\rightarrow \) 0. The theory was soon generalized by Gor'kov, using thermodynamic field theory, to derive[1]} the much used 1950 phenomenological free energy theory of Ginzburg and Landau.[2]} This extension of theory also provided a direction for pursuing necessary developments, especially a microscopic understanding of total electron-electron interactions in metals, a path that is discussed in subsections below.
